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A001725
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n!/5!.
(Formerly M4243 N1772)
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30
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1, 6, 42, 336, 3024, 30240, 332640, 3991680, 51891840, 726485760, 10897286400, 174356582400, 2964061900800, 53353114214400, 1013709170073600
(list; graph; refs; listen; history; internal format)
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OFFSET
| 5,2
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COMMENTS
| The asymptotic expansion of the higher order exponential integral E(x,m=1,n=6) ~ exp(-x)/x*(1 - 6/x + 42/x^2 - 336/x^3 + 3024/x^4 - 30240/x^5 + 332640/x^6 - 3991680/x^7 + ...) leads to the sequence given above. See A163931 and A130534 for more information. [Johannes W. Meijer, Oct 20 2009]
a(n) = A173333(n,5). [From Reinhard Zumkeller, Feb 19 2010]
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REFERENCES
| Mitrinovic, D. S.; Mitrinovic, R. S.; Tableaux d'une classe de nombres relies aux nombres de Stirling. II. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 107-108 1963 1-77.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 5..300
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 265
W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
Alexsandar Petojevic, The Function vM_m(s; a; z) and Some Well-Known Sequences, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.7
Index to divisibility sequences
Index entries for sequences related to factorial numbers
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FORMULA
| E.g.f.: x^5/(1-x)^6.
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MATHEMATICA
| lst={}; Do[AppendTo[lst, n!/5! ], {n, 5, 5!}]; lst [From Vladimir Orlovsky, Oct 25 2008]
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PROG
| (PARI) a(n)=n!/120 \\ Charles R Greathouse IV, Jul 19 2011
(MAGMA) [Factorial(n)/120: n in [5..25]]; // Vincenzo Librandi, Jul 20 2011
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CROSSREFS
| a(n)= A049374(n-4), n >= 1 (first column of triangle). Cf. A049460, A051339. a(n)= A051338(n-5, 0)*(-1)^(n-1) (first unsigned column of triangle).
Sequence in context: A082302 A144223 A029588 * A123510 A132804 A074017
Adjacent sequences: A001722 A001723 A001724 * A001726 A001727 A001728
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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